Development of frequency-dependent DC equivalent models for multi-terminal DC grids

Abstract

The emergence of Multi-Terminal DC (MTDC) grids for offshore wind integration introduces challenges in modeling dynamic interactions and ensuring HVDC system stability. Accurate AC and DC grid equivalents are essential for converter compliance testing and control design, especially in a multi-vendor context, where interoperability issues may arise. This paper proposes two DC grid equivalent models: a simple RLC-based model for low-frequency dynamics, and a reduced-order frequency-dependent model (from order 47 to 5) to capture both low and high frequency behavior based on DC-grid impedance fitting. The two models can effectively capture different DC grid variations, such as variations in DC Reactor (DCR) size, control modes, and operating points. Their applicability is demonstrated through frequency-domain impedance analysis and time-domain simulations of a 3-terminal DC grid with detailed MMC models. A case study is presented to highlight the importance of representing higher frequency dynamics for stability analysis. In addition, the frequency-dependent model is implemented in time-domain simulations to bridge the gap between stability analysis in the frequency and time domains.

Mohamed Elsodany, Kosei Shinoda, Jing Dai, Seddik Bacha

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Published in International Journal of Electrical Power & Energy Systems
Volume 173, December 2025, 111427